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The relationship between synchronization and percolation for regular networks

Author

Listed:
  • Li, Zhe
  • Ren, Tao
  • Xu, Yanjie
  • Jin, Jianyu

Abstract

Synchronization and percolation are two essential phenomena in complex dynamical networks. They have been studied widely, but previously treated as unrelated. In this paper, the relationship between synchronization and percolation are revealed for regular networks. Firstly, we discovered a bridge between synchronization and percolation by using the eigenvalues of the Laplacian matrix to describe the synchronizability and using the eigenvalues of the adjacency matrix to describe the percolation threshold. Then, we proposed a method to find the relationship for regular networks based on the topology of networks. Particularly, if the degree distribution of the network is subject to delta function, we show that only the eigenvalues of the adjacency matrix need to be calculated. Finally, several examples are provided to demonstrate how to apply our proposed method to discover the relationship between synchronization and percolation for regular networks.

Suggested Citation

  • Li, Zhe & Ren, Tao & Xu, Yanjie & Jin, Jianyu, 2018. "The relationship between synchronization and percolation for regular networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 492(C), pages 375-381.
    • Handle: RePEc:eee:phsmap:v:492:y:2018:i:c:p:375-381
    DOI: 10.1016/j.physa.2017.10.003
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    Cited by:

    1. Lin, Jianjun & Chen, Huisu & Liu, Lin & Zhang, Rongling, 2020. "Impact of particle size ratio on the percolation thresholds of 2D bidisperse granular systems composed of overlapping superellipses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    2. Guo, Lei & Liu, Chengjun & Wu, Youxi & Xu, Guizhi, 2023. "fMRI-based spiking neural network verified by anti-damage capabilities under random attacks," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).

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